High-Dimensional Geometry in Signal Processing

Organizers: Richard Baraniuk, Hyeokho Choi, Alfred Hero III, Robert Nowak

A major and fundamental issue we face today is how to constructively and efficiently analyze and process the plethora of measured signals and information. Medical and biological measurement systems, computer networks and wireless communication systems, and remote sensing and imaging systems provide us with information-bearing signals from a myriad of sources and sensors that must be transmitted, fused, stored, analyzed and interpreted effectively and in a computationally tractable manner. In short, we face a challenging task -- analyzing and processing more high-dimensional data and information than ever before.

This special session will explore the reaches of signal processing techniques in such problems with high-dimensional data. A central theme is learning and/or exploiting a lower-dimensional manifold structure in the data, often resulting from some kind of geometrical structure. For examples, edges in images can be thought of as 1-d curves embedded in the 2-d image space, decision boundaries in classification problems are (d-1) dimensional manifolds in d-dimensional feature spaces, and often very high-dimensional observations are related to one another through low-dimensional physical transformations, for instance in problems of face recognition or speaker identification.

Regular lectures:

• Title: Estimating Dependency Measures and their Significance for High-Dimensional Data Sources
  Authors: Mike Siracusa, Alexander Ihler, John Fisher III, Alan Willsky, MIT
• Title: Iterative Denoising via Maximization of Mutual Information for Unsupervised Classification
  Authors: Damianos Karakos, Sanjeev Khudanpur, Carey Priebe, Johns Hopkins University
• Title: Local Manifold Learning
  Authors: Hongyuan Zha, Zhenyue Zhang, Pennsylvania State University
• Title: Graph Based Divergence Estimators for High Dimensional Data Analysis
  Authors: Jose Costa and Alfred Hero III, University of Michigan
• Title: Level Set Estimation via Trees
  Authors: Rebecca Willett and Robert Nowak, University of Wisconsin
• Title: Multiscale Projections for Articulation Manifolds
  Authors: Michael Wakin, David Donoho, Hyeokho Choi, Richard Baraniuk, Rice University and Stanford University